Complete the Prime Number: What Digit Fills in the Blank for _7?

Q: How do I quickly check if a two-digit number is prime?

Test divisibility by small primes: 2, 3, 5, 7. If your number isn't divisible by any of these, it's likely prime! For numbers ending in 7 like our candidates, you only need to check odd divisors.

Q: Why isn't 27 prime if it's not even?

Being odd doesn't make a number prime! $ 27 = 3 \times 9 $, so it has factors other than 1 and itself. Always check divisibility by all small primes, not just 2.

Q: What's the fastest way to check if 17 is prime?

Since $ \sqrt{17} \approx 4.1 $, you only need to test divisibility by primes ≤ 4: that's just 2 and 3. Since 17 ÷ 2 = 8.5 and 17 ÷ 3 = 5.67..., neither divides evenly, so 17 is prime!

Q: How do I remember which small numbers to test for divisibility?

Use the first few primes: 2, 3, 5, 7, 11, 13... For two-digit numbers, testing up to 7 usually covers most cases. Make it a habit to check these in order!

Prime Number Identification with Two-Digit Numbers

Fill in the blanks for a prime number:

$\square7$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the blanks for a prime number:

$\square7$

Step-by-step solution

To solve the problem, we must identify which digit replaces the placeholder in $\square7$ to make a prime number. The choices provided are $1, 2, 5,$ and $7$ .

Let's test each choice:

Substitute $1$ : The number becomes $17$ . Check if it's prime.
Substitute $2$ : The number becomes $27$ . Check if it's prime.
Substitute $5$ : The number becomes $57$ . Check if it's prime.
Substitute $7$ : The number becomes $77$ . Check if it's prime.

Let's evaluate each result:

$17$ : $17$ is not divisible by any number, hence it is prime.
$27$ : Not prime (divisible by $3$ ).
$57$ : Not prime (divisible by $3$ ).
$77$ : Not prime (divisible by $7$ ).

Therefore, the only prime number formed is $17$ .

Thus, the correct digit that makes the number $\square7$ a prime number is $1$ , and the complete number is $17$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime numbers have exactly two factors: 1 and themselves
Testing: Check divisibility by small primes like 2, 3, 5, 7
Verification: Confirm $17$ has no divisors between 1 and 17 ✓

Common Mistakes

Avoid these frequent errors

Not checking all possible divisors systematically
Don't just guess if a number is prime without testing divisibility! This leads to wrong conclusions like thinking 27 or 57 might be prime. Always test divisibility by prime numbers up to the square root of your candidate number.

Practice Quiz

Test your knowledge with interactive questions

Which of the numbers is a prime number?

FAQ

Everything you need to know about this question

How do I quickly check if a two-digit number is prime?

Test divisibility by small primes: 2, 3, 5, 7. If your number isn't divisible by any of these, it's likely prime! For numbers ending in 7 like our candidates, you only need to check odd divisors.

Why isn't 27 prime if it's not even?

Being odd doesn't make a number prime! $27 = 3 \times 9$ , so it has factors other than 1 and itself. Always check divisibility by all small primes, not just 2.

What's the fastest way to check if 17 is prime?

Since $\sqrt{17} \approx 4.1$ , you only need to test divisibility by primes ≤ 4: that's just 2 and 3. Since 17 ÷ 2 = 8.5 and 17 ÷ 3 = 5.67..., neither divides evenly, so 17 is prime!

Are there any patterns for numbers ending in 7?

Numbers ending in 7 can be prime (like 7, 17, 37, 47) but aren't automatically prime (like 27, 57, 87). You still need to test each one individually for divisibility.

How do I remember which small numbers to test for divisibility?

Use the first few primes: 2, 3, 5, 7, 11, 13... For two-digit numbers, testing up to 7 usually covers most cases. Make it a habit to check these in order!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime